1. Computed Tomography Image Reconstruction

2. Reconstruction Input: Raw Data
255
199
712
Intensity (transmission) measurements
534
417
364
501

3. Image Reconstruction Output: Image Data
Individual pixel values (question marks) ?

4. Algorithm
Set of calculation rules for getting a specific output (answer) from a specific input
Reconstruction algorithm examples
Back projection
Filtered back projection
Interpolation

5. Back Projection Reconstruction63 ? ? ? ? ? ? ?
Reconstruction Problem
converting transmission data for individual projections into attenuation data for each pixel

6. Back Projection Reconstruction
for given projection, assume equal attenuation for each pixel
repeat for each projection adding results 63 9 9 9 9 9 9 9

7. Back Projection Reconstruction
Assume actual image has 1 hot spot (attenuator)
Each ray passing through spot will have attenuation back-projected along entire line
Each ray missing spot will have 0’s back-projected along entire line 63
Hot Spot 9 9 9 9 9 9 9

8. Back Projection Reconstruction
Each ray missing spot stays blank
Each ray through spot shares some density
Location of spot appears brightest 63 9 9 9 9 9 9 9
Hot Spot

9. Back Projection Reconstruction
Streaks appears radially from spot
star artifact
Star Artifact Spokes
Hot
Spot

10. Filtered Back Projection*
enhancement of back projection technique
filtering function (convolution) is imposed on transmission data
small negative side lobes placed on each side of actual positive data
negative values tend to cancel star artifact
Unfiltered back projection
Filtered back projection

11. Filtered Back Projection
Operationally fast
reconstruction begins upon reception of first transmission data
Commercially used reconstruction algorithm for decades
Now being replaced by iterative

12. “It All Adds Up” Puzzle www.education-world.com/a_lesson/italladdsup
Iterative Reconstruction
“It All Adds Up” Puzzle 17 2 5 6 4 9 1 22 16 19 7 9 23 15 17 14

13. This is what your CT Scanner must solve!13
Slightly
harder? 22 12 10 15 16 22 11 10 17

14. Real Problem Slightly More Complex
***
100’s of 100’s of angles 14
512 values
512
values
m11
m12
m13
m14
m21
m22
m23
m24
m31
m32
m33
m34
m41
m42
m43
m44 35 13 22 9 24 13 15 22 16

15. Iterative Reconstruction
calculate difference between measured & calculated attenuation for next projection
correct pixels equally for current projection to achieve measured attenuation BUT!!!

16. Iterative Reconstruction
Correcting pixels for one projection alters previously-calculated attenuation for others
corrections repeated for all projections until no significant change / improvement

17. Iterative Reconstruction
Start with measured data 12 15 9
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? ? ?
? ? ? 17 19 12
Measurements

18. Iterative Reconstruction
Make initial guess for first projections by assuming equal attenuation for each pixel in a projection
Similar to back projection 12 15 9
Measurements
? ? ?
? ? ?
? ? ? 17 19 12
Initial guess based
upon vertical projections
Measurements

19. Iteration Example 8 4 4 24 12 12 Initial guess based
Initial guess based
upon vertical projections 17 19 12
Low by 1; add .33 to each.
Make corrections
based on
horizontal
Projections data
Low by 3; add 1 to each.
High by 4; subtract 1.33 from each.

20. Iteration Example 17 19 12 9 15 12
Make corrections
based upon
Data measured on
diagonals
High by .33; subtract .17 from each.
High by 1; subtract .33 from each.
Low by .3; add .17 to each.

21. Iterative Reconstruction: General Electric Adaptive Statistical Iterative Reconstruction (ASIR)
Claims & Observations
22-66% reduction in dose in abdominal scans with no change in spatial or temporal resolution
Algorithm creates different texture
Appears artificial
Creates a “new normal”

22. Iterative Reconstruction: Siemens Iterative Reconstruction in Image Space (IRIS)
Claims & Observations
Dose reduction up to 60% without quality loss
Fast reconstruction

23. Iterative Reconstruction: Philips iDose
Claims & Observations
Dose reduction for coronary CT angiography more than 80% without quality loss
Reconstruction times of up to 20 images/second
Can improve image quality in typically high noise bariatric exams

24. Multi-plane reconstruction
using data from multiple axial slices it is possible to obtain
sagittal & coronal planes
oblique & 3D reconstruction
Non-spiral reconstruction
Poor appearance if slice thickness >>pixel size
multi-plane reconstructions are computer intensive

25. 3D Reconstructions Uses pixel data from multiple slices
Algorithm identifies surfaces & volumes
Display renders surfaces & volumes
Real-time motion
auto-rotation
user-controlled multi-plane rotation

26. 3D Reconstructions